# Scientific Challenges by Computation

Graduate course at KTH Spring 07

The purpose of the course is to develop attitudes of critical thinking and questioning of established scientific doctrines, by working with set of challenges of mathematical modeling in science and engineering including

- d'Alembert's paradox
- Sommerfeld's paradox
- Loschmidt's paradox
- Gibbs' paradox
- black body radiation
- quantum mechanics
- relativity theory
- arrow of time.

Basic theoretical material for the course is available on my home page in the form of books and articles related to the topics 1-7. Software for computation is available on Fenics. See also the home page for the new book Computational Turbulent Incompressible Flow.

The essense of this material is that computation offers new possibities of resolving classical open problems in science and engineering. The basic principle is a combination of finite precision computation with (a posteriori) output stability estimation, referred to as General Galerkin or G2, following the idea that physics is (some form of) analog computation or information processing, which can be simulated by digital computation.

The course will be given in a new form, where the students organize into (non-disjoint) subgroups, each of which approaches one of the topics 1-7 towards the goal of developing a wiki including

- presentation of the paradox/problem
- presentation and analysis of classical resolutions
- presentation and analysis of new resolutions
- (possibly) presentation and analysis of even newer resolutions.

The whole group of students then puts the results together to a wiki for the whole course covering 1-7 (or a subset thereof).

A specific aim with the course is to test the new possibilities of active learning and cooperative work opened by wiki.

The whole group will meet once a week in a seminar for discussion and presentation of work progress.

The course may be of interest to Ph D students in computational mathematics, mechanics and physics.

Students deciding to follow the course should send an email to me (claes@math.chalmers.se) and indicate possible times for the seminar.

Wellcome

Claes Johnson